If you do not have the factory 12v socket option installed (for USA bikes) you can use the plug under the seat for power, and use a relay to trigger the brake part tapping into the brake wires in the 6 pin plug to the rear assembly (also under the seat on the left side frame tube). Even if you do have the 12v socket installed you can tap into that to provide the power for the top case lights since they should be LED and the 10 amp circuit is unlikely to be overloaded for that. I usually don't like to tap into any factory wiring or circuits that are already in use on a bike to provide any power for what I add but this is one option that is not likely overloaded for that. Just don't use those blue crimp on splicers that you clamp on with pliers since those actually damage the wire strands. Posi-Taps are OK if you want easy. Then use any good connector you wish to run a cable to the top case so you can easily unplug if/when you take the top case off. Keep all connections under the seat to protect from weather.
You'll want to power your additional lights directly from the lights they're imitating. That is, get the power for the running lights off your tail light or plate illuminator and the brake light power from your brake light circuit. I recommend using Posi-Tap connectors, they're inexpensive and dead reliable.
Let me reiterate...
DO NOT get POWER for you added lights from any factory circuit if at all possible. This WILL eventually cause problems. BTDT and had to repair the factory wire harness and relays for my Gold Wing due to the PO getting power from factory wires for extra lights. Isolate the power for any added lighting by using a relay and only TRIGGER that relay on/off from a factory wire (relay trigger load is so small as to present almost no load on factory wires). If there is ever a problem with what you added you won't spend big bucks to repair factory electrics this way. I only suggested using the 12v socket wires for power since most CTX1300 bikes in the USA come from the factory without that option installed. And even if it is installed it is usually not used for anything significant and yet has heavier wires to carry more load. Personally I got power directly from the battery with a wire pair (ground and +12v) that I ran back to the area under the seat to run a light bar I added in back. There is at least one member here from the earliest years of the forum who burned out the rear turn signals by connecting a module directly to the factory wire harness (he was promised by the vendor the module works with LED lights, but that vendor was talking of LED replacement bulbs and not factory designed LED light assemblies) and found out the hard way just how very expensive the rear light assembly can be. And that rear light assembly is a single sealed unit... no individual lamp repair/replace possible.
Bob's right of course, my answer was incomplete. Power them from the accessory circuit or some other auxiliary circuit you've added, *trigger* that power through a relay with the current going to to the lamp. 12V relays are cheap and easy to wire up, and you can find mini or micro ones that are quite easy to stash.
@Duff that device is pretty slick.. all self contained and compact. Of course since it is all self contained, when one part fails, I'm guessing the whole thing fails.. but there are always trade offs. I added it to the knowledge sharing doc.
Kind of a busy weekend ! I powered the running lights for the trunk, installed a cable for my gerbing jacket and and an USB charger in the handlebars for my iphone.
Since the trunk had only running lights, I took power from the under the seat accessory cable; I tap into it and soldered it.
I connected to the battery the gerbing cable fished it so the connector comes on the side of the seat; then I tapp into this cable behind the fuse to connect the USB charger.
Next, I will connect -somewhere- a cigarette lighter. I will also connect a relay to power a small led bar for brake lights and finally aux lights.. so I still have a bunch to do !